Avoir or être

Esther, 

this is not the reflexive (pronominal) verb " s'embrasser ", but the standard verb " embrasser ' preceded by the direct object ' me ", with the subject being 'elle'. ‘Embrasser’ conjugates in compound tenses with ‘avoir’. 

In other words, this is not a reciprocal action. In English, this is "she kissed me" ( and 'me' is male, as determined by the French past participle ), not "we kissed each other". 

The reciprocal statement in French, requiring the pronominal, would be " on s'est embrassés " or ' nous nous sommes embrassés ' - 'we kissed each other'.

Difficult I know, but a number of verbs can be in standard or pronominal form, and the context and conjugation of the verb both convey information.

 https://kwiziq.learnfrenchwithalexa.com/revision/glossary/voice/la-voix-pronominale 

https://www.larousse.fr/dictionnaires/francais/embrasser/28656

https://www.wordreference.com/fren/embrasser